In this talk we consider continuous time random walks on $\mathbb{Z}^d$ among random conductances that permit jumps of arbitrary length, where the law of the conductances is assumed to be stationary and ergodic. Under a suitable moment condition we obtain a quenched local limit theorem and Hölder regularity estimates for solutions of the heat equation for the associated non-local discrete operator. Our results apply to random walks on long-range percolation graphs with connectivity exponents larger than 2d when all nearest-neighbour edges are present. This talk is based on a joint work with Martin Slowik (Mannheim).